Because he is taking it for granted that a biological complex that performs a specific function is purposeful, which implies intention. And then he says that this implies intelligence, ie 'a purposeful arrangement of parts proves that the parts were arranged purposefully'. It's not wrong, it just doesn't go any way to proving his point.

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Frankly, I don't know what he means when he says that life is an axiom and unsolvable within science.

Me neither.

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But it is life that it is well arranged for. It's looking like the whole inanimate world lends support to the animate world.

Maybe my physics is lacking but I don't see how that in any way is scientific proof that it was set up by an intelligent force, and even if it is that does not have any bearing on evolution. If fundemental laws are found that affect in some part how evolution has played out, this will not prove the ID claim that an intelligence actively interferes with evolution.